Partially semi-transparent texture in Cycles
The general way you want to do this is by using the mix shader node to mix between your "solid" shader output (diffuse, glossy, principled, any shader you want) and a transparent chader node. By plugging the alpha channel of your image into the "Fac" setting of the mix shader node, the alpha channel of the image lets you control how transparent the result is. The alpha channel is what changes when you make parts of your image transparent in Photoshop. You can also use nodes like the noise or Musgrave texture nodes to procedurally generate transparent and opaque portions of the object. Just plug the factor output to the factor input on the mix shader node.

See this post for an example.